Ryan is packing books into a rectangular box. all the books are the same size the book's height is 6, width is 15, length is 20cm the box height is 20 cm, width is 30 cm, length is 36cm how many books can fit inside the box

The statement is valid because the measure of the vertices located in the center of the pentagon is the quotient of 360 and 5, and the sum of two base angles in the given isosceles triangle is 108.

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Explanation:

Check out the diagram below. I have added x and y such that

x = base angle

y = vertex angle (located adjacent to center of polygon)

The pentagon is sliced up like a cake into 5 equal portions. Each vertex angle is y = 360/5 = 72 degrees.

The two base angles x must add with the vertex angle y to get 180

(angle1)+(angle2)+(angle3) = 180

x+x+y = 180

2x+y = 180

2x+72 = 180

2x = 180-72

2x = 108

This is true for any one of the five triangles. Notice that for angle LMN, we can divide it into LMQ and QMN where Q is the center of the polygon. Both of these angles are x. Since we've shown 2x = 108, we can see that LMN must also be 108 as well.

Choice A is close, but we wouldn't use the exterior angle theorem. Choice B is the better answer.

Answer:

The answer is below.

Step-by-step explanation:

PROVE √(1-〖cos〗^2 θ)/cosθ = tanθ

Now 1 - cos^2 θ = sin^2θ

So  √(1 - cos^2 θ) = sin θ

and  √(1 - cos^2 θ) / cos  θ

= sin θ / cos θ

= tan θ

Step-by-step explanation:

[tex]\dfrac{\sqrt{1-\cos^2\theta}}{\cos\theta}=\tan\theta\\\\\text{We know:}\\(1)\ \sin^2x+\cos^2x=1\to\sin^2x=1-\cos^2x\\(2)\tan x=\dfrac{\sin x}{\cos x}\\\\\text{For}\ \sqrt{1-\cos^2\theta}\ \text{use}\ (1):\\\\L_S=\dfrac{\sqrt{1-\cos^2\theta}}{\cos\theta}=\dfrac{\sqrt{\sin^2\theta}}{\cos\theta}=\dfrac{\sin\theta}{\cos\theta}=\tan\theta\ \ \ _{used (2)}\\\\R_S=\tan\theta\\\\L_S=R_S[/tex]

[tex]\text{Of course, this equality is not true for everyone values of}\ \theta.\\\\1^o.\ \cos\theta\neq0\to\theta\neq\dfrac{\pi}{2}+k\pi,\ k\in\mathbb{Z}\\\\2^o.\ \sqrt{\sin^2\theta}=|\sin\theta|,\ \text{therefore}\\\\\text{for}\ \theta\in[2k\pi;\ (2k+1)\pi],\ \sin\theta\geq0\to|\sin\theta|=\sin\theta\\\\\text{therefore}\ \dfrac{|\sin\theta|}{\cos\theta}=\dfrac{\sin\theta}{\cos\theta}=\tan\theta[/tex]

[tex]\text{for}\ \theta\in\bigg((2k-1)\pi;\ 2k\pi\bigg),\ \sin\theta<0\to|\sin\theta|=-\sin\theta\\\\\text{therefore}\ \dfrac{|\sin\theta|}{\cos\theta}=\dfrac{-\sin\theta}{\cos\theta}=-\tan\theta\neq\tan\theta[/tex]

[tex]\text{Conclusion:}\\\\\text{This equality is true for}\ \theta\in\left[2k\pi;\ \dfrac{\pi}{2}+2k\pi\right)\cup\left(\dfrac{\pi}{2}+2k\pi;\ \pi+2k\pi\right],\ k\in\mathbb{Z}[/tex]

Answer:

hope this helps :)

Step-by-step explanation:

.......

Answer:

1225

Step-by-step explanation:

Please see attached picture for full solution.

Answer:

  1

Step-by-step explanation:

Use the form for the factoring of the sum of cubes.

To make this easier to write, we'll use the substitutions ...

  a = sin(θ), b = cos(θ)

It looks like you may want to simplify ...

  (a³ +b³)/(a +b) +ab

  = ((a +b)(a² -ab +b²))/(a +b) +ab

The factors of (a+b) cancel. In this case, we know that a² +b² = 1, so this becomes ...

  = (1 -ab) +ab

  = 1

  [tex]\boxed{\dfrac{\sin^3{\theta}+\cos^3{\theta}}{\sin{\theta}+\cos{\theta}}+\sin{\theta}\cos{\theta}=1}[/tex]

Answer:

surface area of sphere = 615.44mm²

volume of sphere = 523.33mm³

Step-by-step explanation:

S.A = 4πr²

4 × 3.14 × 7 × 7 = 615.44.

volume = 4πr³/3

4 × 3.14 ×5 × 5 × 5 ÷ 3 = 523.33

Answer:

a) More.

b) Less.

c) More.

Step-by-step explanation:

a) If you invest $10 with an interest rate of 50% (that's very high I know XD), you would earn 10 / 2 = $5 in interest. If you invest $100 with an interest rate of 50%, you would earn 100 / 2 = $50 in interest. So, the more principal invested, the more interest earned.

b) Let's say you are investing $100. If there is an interest rate of 50%, as stated before, you would earn $50 in interest. If the interest rate were lowered to 25%, you would earn 100 / 4 = $25 in interest. So, the lower the interest rate, the less the interest.

c) The same exact thing as part a.

Hope this helps!

Answer:

D. 1, 3, 5, 15

Step-by-step explanation:

Factors are numbers that divide another number evenly, with no remainders.

15 ÷ 1 = 15

15 ÷ 3 = 5

15 ÷ 5 = 3

15 ÷ 10 = 1.5

15 ÷ 2 = 7.5

15 ÷ 15 = 1

The numbers that 15 divide evenly into are 1, 3, 5, and 15.

Hope that helps.

Answer:

The data that we have is:

Price per item = $25

spending limit = $200

Now, if you sell x items, then your earnings will be:

E = $25*x

So if you sell two items, we have x = 2

E(2) = $25*2 = $50

But the maximum spending possible will be such that:

$25*x = $200

x = $200/$25 = 8

Then the equation is:

E(x) = $25*x

such that  0 ≤ x ≤ 8

Which means that you can sell any number of units between 0 and 8.

Answer:

Z = 0.87

Explanation:

Given the following data;

Sample 1:

n1 = 30

Mean, X = 2.36

Standard deviation, Ox = 0.96

Sample 2:

n2 = 60

Mean, Y = 2.19

Standard deviation, Oy = 0.66

The formula for test statistics for two population is;

[tex]Z = \frac{X-Y}{\sqrt{(\frac{Ox^2} {n_1} } +\frac{Oy^2}{n_2} )}}[/tex]

Substituting the values, we have;

[tex]Z = \frac{2.36-2.19}{\sqrt{(\frac{0.96^2} {30} +\frac{0.66^2}{60} )}}[/tex]

[tex]Z = \frac{0.17}{\sqrt{(\frac{0.9216} {30} +\frac{0.4356}{60} )}}[/tex]

[tex]Z = \frac{0.17}{\sqrt{(0.03072 +0.00726)}}[/tex]

[tex]Z = \frac{0.17}{\sqrt{0.03798}}[/tex]

[tex]Z = \frac{0.17}{0.19488}[/tex]

Z = 0.8723

The test statistics to 2 d.p is 0.87

Therefore, Z = 0.87

Answer:

C

Step-by-step explanation:

Answer:

410.4

136.8

Step-by-step explanation:

Because the post office processes 45.6 letters every hour and is open 9 days an hour, it processes 45.6*9, or 410.4 letters per day.  Because it is open on Christmas for 3 hours more than normal days(12-9), it produces 45.6*3, or 136.8 more letters on Christmas.

Hope it helps <3

Answer:

A. 410.4 letters

B. 136.8 more letters

Step-by-step explanation:

1.

We know that the post office processes 45.6 letters per hour. If we want to know how many letters they process in 9 hours, we can multiply 45.6 and 9.

45.6 * 9

Multiply

410.4

The post office can process 410.4 letters in 9 hours, therefore A is correct.

2.

The post office still process 45.6 letters per hour, but they are open for 12 hours. First, multiply 12 and 45.6.

12 * 45.6

547.2

We are asked to find how many more letters they can process. We need to find the difference between the letters they normally process and the letters they process on Christmas.

Christmas - normal

They process 547.2 on Christmas and 410.4 normally.

547.2 - 410.4

136.8

They process 136.8 more letters on Christmas. Therefore, choice B is correct. Thank

Answer:

I think it's a

Step-by-step explanation:

Because this would ddetermine if the software lab is successfull working.

Answer:

Increase.

Step-by-step explanation:

Let's say p=25.

50/25=2

If p decreased and we turned the 25 into a 2, then 50/2=25.

The answer increased.

I hope this is what you were looking for!! <3

Answer:

The height of the cylinder is 4 x units.

The area of the cylinder’s base is One-fourthπx2 square units

Step-by-step explanation:

Formula for volume of the cylinder:

V = r² π h

Volume of the cylinder=

πx^3

Diameter=x

Radius (r)=diameter/2

=x/2

V = r² π h

πx^3=(x/2)^2πh

πx^3=(x^2/4)πh

Divide both sides by π

x^3=(x^2/4)h

Make h the subject of the formula

h=x^3÷x^2/4

=x^3×4 / x^2

=4x^3 / x^2

=4*x*x*x / x*x

h=4x

Area of the base:

B = r² π

Recall, r=x/2

B=(x/2)^2 * π

=(x^2/4)π

=πx^2/4

=1/4(πx^2)

The area of the cylinder’s base is One-fourthπx2 square units.

Answer:

B & E

Step-by-step explanation:

Edge 2020

Answer:

72º

Step-by-step explanation:

Hey there!

Well the interior of a pentagon's angle is 108º,

so we do,

180 - 108 = 72º

Hope this helps :)

Answer:

72°

Step-by-step explanation:

→ First find the measure of all interior angle, utilise the formula (n-2) × 180° where n is the number of sides

(n-2) × 180° ⇔ (5-2) × 180° ⇔ 3 × 180° ⇔ 540°

→ 540° is the total sum of the angles in the pentagon, divide this by 5 to get one of the interior angles

540° ÷ 5 = 108°

→ Now, remember the fact that 1 interior + 1 exterior angle = 180°

180 - ( 1 interior angle ) → 180 - (108) = 72°

Answer:     .28

Step-by-step explanation:

.3+.42= .72

1-.72=.28

Answer:

0.28

Step-by-step explanation:

The sum of a list of probabilities = 1

Sum of given probabilities = 0.72

So, probability of getting pasta = 1-0.72 = 0.28

Hope this helps

Answer:

the third graph is correct

Step-by-step explanation:

edge

the second part is x<1

Answer:

the third graph and the send part it is x<1

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (0, - 6) and (x₂, y₂ ) = (8, - 4) ← 2 points on the line

m = [tex]\frac{-4+6}{8-0}[/tex] = [tex]\frac{2}{8}[/tex] = [tex]\frac{1}{4}[/tex]

The line crosses the y- axis at (0, - 6 ) ⇒ c = - 6

y = [tex]\frac{1}{4}[/tex] x - 6 → B

Answer:?

Step-by-step explanation:

Step-by-step explanation:

The figure above is a cube since all it's sides are equal

Volume of a cube = l³

where l is the length of one side

From the question

l = 5

So the volume of the cube is

Volume = 5³

Surface area of a cube = l²

= 5²

Hope this helps you

Answer:

Your answer is correct

Step-by-step explanation:

(2^5/4)² = 4^5/2 = √4^5

The correct answer is option B which is [tex]\sqrt{2^5}[/tex].

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

The expression will be solved as follows:-

[tex]E = ([ 2^{\frac{1}{2}} \times 2^{\frac{3}{4}}])^2\\E = (2^{({\frac{1}{2}+\frac{3}{3}})})^2\\E = (( 2 )^ {\frac{5}{4})}^2 \\E = ( 2 ) ^{\frac{5}{2}}\\E = \sqrt{2^5}[/tex]

Therefore the correct answer is option B which is [tex]\sqrt{2^5}[/tex].

To know more about Expression follow

https://brainly.com/question/723406

#SPJ5

Answer:

The percentage that of people who gave the movie a rating between 6.8 and 8.8

P(6.8≤X≤8.8)  = 83.9≅ 84 percentage

Step-by-step explanation:

Step(i):-

Mean of the Population = 8.3 points

Standard deviation of the Population = 0.5 points

Let 'X' be the random variable in normal distribution

Let X = 6.8

[tex]Z = \frac{x-mean}{S.D} = \frac{6.8-8.3}{0.5} = -3[/tex]

Let X = 8.8

[tex]Z = \frac{x-mean}{S.D} = \frac{8.8-8.3}{0.5} = 1[/tex]

The probability that of people who gave the movie a rating between 6.8 and 8.8

P(6.8≤X≤8.8) = P(-3≤Z≤1)

                     = P(Z≤1)- P(Z≤-3)

                    =  0.5 + A(1) - ( 0.5 -A(-3))

                   = A(1) + A(3)       (∵A(-3)=A(3)

                  =  0.3413 +0.4986    (∵ From Normal table)

                 = 0.8399

Conclusion:-

The percentage that of people who gave the movie a rating between 6.8 and 8.8

P(6.8≤X≤8.8)  = 83.9≅ 84 percentage

Answer:

i think its 42.77... might be wrong tho

Step-by-step explanation:

being marked down by 60 percent means to multiply original number by 0.4

so we get 39.6

the multiply it by 1.08 to get 42.768

Answer:

See below.

Step-by-step explanation:

To find the marked down price, multiply the total by the percentage.

[tex]99*.6=59.4[/tex]

Next, subtract the amount from the total.

[tex]99-59.4=39.6[/tex]

Then, multiply to find the sales tax.

[tex]39.6*0.08=3.168[/tex]

[tex]39.6+3.168=42.768[/tex]

Answer: $42.77

Answer:

1/4

Step-by-step explanation:

Answer:

[tex] 4\sqrt{3} [/tex]

[tex] \dfrac{5 - \sqrt{3}}{11} [/tex]

[tex] \dfrac{11(3 + \sqrt{5})}{8} [/tex]

Step-by-step explanation:

If you have a simple square root in the denominator, multiply the fraction by a fraction that is the root over the root.

[tex] \dfrac{12}{\sqrt{3}} = [/tex]

[tex] = \dfrac{12}{\sqrt{3}} \times \dfrac{\sqrt{3}}{\sqrt{3}} [/tex]

[tex]= \dfrac{12\sqrt{3}}{\sqrt{3}\sqrt{3}}[/tex]

[tex] = \dfrac{12\sqrt{3}}{3} [/tex]

[tex] = 4\sqrt{3} [/tex]

If you have a denominator consisting of a rational number plus a root, multiply the fraction by a fraction that is the denominator over the denominator in which you change only the sign outside the root.

[tex] \dfrac{2}{5 + \sqrt{3}} = [/tex]

[tex] = \dfrac{2}{5 + \sqrt{3}} \times \dfrac{5 - \sqrt{3}}{5 - \sqrt{3}} [/tex]

[tex] = \dfrac{2(5 - \sqrt{3})}{(5 + \sqrt{3})(5 - \sqrt{3})} [/tex]

[tex] = \dfrac{2(5 - \sqrt{3})}{25 - 3} [/tex]

[tex] = \dfrac{2(5 - \sqrt{3})}{22} [/tex]

[tex] = \dfrac{5 - \sqrt{3}}{11} [/tex]

[tex] \dfrac{11}{6 - 2\sqrt{5}} = [/tex]

[tex] = \dfrac{11}{6 - 2\sqrt{5}} \times \dfrac{6 + 2\sqrt{5}}{6 + 2\sqrt{5}} [/tex]

[tex] = \dfrac{11(6 + 2\sqrt{5})}{(6 - 2\sqrt{5})(6 + 2\sqrt{5})} [/tex]

[tex]= \dfrac{22(3 + \sqrt{5})}{36 - 4 \times 5}[/tex]

[tex] = \dfrac{22(3 + \sqrt{5})}{36 - 20} [/tex]

[tex] = \dfrac{22(3 + \sqrt{5})}{16} [/tex]

[tex] = \dfrac{11(3 + \sqrt{5})}{8} [/tex]

Answer:

see attached

Step-by-step explanation:

Answer: No

Step-by-step explanation:

No, because 4^2 is 16, 8^2 is 64, 10^2 is 100 and 16+64 = 80 and 80≠100

Answer:

c is 35

d is 13

Step-by-step explanation:

I multiplied both sides, and then simplified the equation.

( plz give me brainliest, that would be most appreciated! )

Answer:

D: 9, 12, 15

Step-by-step explanation:

Okay, this one is a very simple and a not so hard question. I understand that teachers prefer kids to not lay out all the terms, but in this case, it won´t be horrible in doing so!

Were going to plug 6 into n, and that will make the formula look like,

F(6)=3(6)-9

18-9=9 so the 6th term is 9

Plug in 7=

F(7)=3(7)-9

21-9=12

The 7th term is 12

Plug in 8=

F(8)=3(8)-9

24-9=15  8th term is 15

That means terms 6, 7, and 8 are: 9, 12, 15

Answer:

D. 9, 12, 15

Answer:

a   8

Step-by-step explanation:

You are given two sides and the included angle. Since you don't have any side and the opposite angle, you must use the law of cosines.

[tex] a^2 = b^2 + c^2 - 2bc\cos A [/tex]

[tex] a^2 = 5^2 + 11^2 - 2(5)(11)\cos 39^\circ [/tex]

[tex] a^2 = 25 + 121 - 110\cos 39^\circ [/tex]

[tex] a^2 = 60.51 [/tex]

[tex] a = 7.779 [/tex]

Answer: a = 8 cm